Often people wonder if the Eucharist may be carried on their person, in
a pocket or purse or even reserved in the home. Not infrequently Eucharistic Ministers
give a Host to someone to take home to a sick person.

Canon 934 forbids reservation of the Blessed Sacrament except in
Tabernacles, and then only as authorized by the bishop. Canon 935 forbids the carrying of
the Blessed Sacrament on one's person, except as required by urgent pastoral need (e.g.
Communion for the sick), and then in accordance with the precepts of the bishop. Canon 910
requires the deputation of the minister of Communion if a lay person. These canons thus
exclude home reservation, travel with the Blessed Sacrament (except to and from a sick
call without any side trips) and the taking of the Sacrament to the sick by individuals
not deputed for that purpose.

As for how the Blessed Sacrament should be transported, the document
"Holy Communion and Worship of the Eucharist outside Mass" says in #20,

The Eucharist for Communion outside a church is to be carried
in a pyx or other covered vessel; the vesture of the minister and the manner of carrying
the Eucharist should be appropriate and in accord with local circumstances. [my emphasis]

It is wrong, therefore, to carry the Blessed Sacrament in some less
dignified way than in the metal container, the pyx or equivalent, made for that purpose.
Further, even putting the pyx in one's pant's pocket or purse is not in keeping with the
dignity of the Blessed Sacrament. The traditional practice of carrying it in a burse
(cloth or leather bag) hung around the neck close to one's heart is both practical and
respectful. Burse's are still made for this purpose; they have not be done away with nor
has the theology of the Eucharist changed permitting casual handling of this August
Mystery.